10/29/12&
how&can&I&find&out&what&%&are&red?&
sta$s$cs&for&designers&
dr.&carman&neustaedter&
what&if&there&are&too&many&to&count?&
how&can&I&find&out&the&%&red?&
count&a&sample&and&generalize&
how&can&we&improve&the&sample?&
take&more&samples&
1&
10/29/12&
variability:&the&difference&between&mul8ple&
measurements&from&a&popula8on&
is&the&%&red&in&one&container&the&same&as&another?&
sta$s$cs&is&about&the&rela8onship&between&samples&
and&a&popula8on&
two&types&of&sta$s$cs&
descrip$ve&stats:&describe&data&
e.g.,&graphs,&variability,&central&tendency&
&
inferen$al&stats:&make&inferences&(conclusions)&
about&the&data&
e.g.,&a&sample&generalizes&to&the&popula8on&
&
&
descrip$ve&stat&examples&
central&tendency&
frequency&distribu$on:&plot&of&how&frequently&
each&value&appears&in&the&data&for&each&level&of&
the&IV&
mean:&add&up&all&measurements,&divide&by&total&
number&of&measurements&
&
median:&the&measurement&with&half&of&the&
measurements&above&it&and&half&below&it&
&
mode:&the&most&frequent&measurement&
2&
10/29/12&
mode?&
median?&
mean?&
mode?&
median?&
mean?&
Frequency&Distribu8on&
6&
5&
4&
3&
2&
1&
0&
7.6&
mode?&
median?&
mean?&
Frequency&Distribu8on&
6&
7.7&
7.8&
7.9&
8&
8.1&
8.2&
8.3&
8.4&
mode?&
median?&
mean?&
5&
4&
3&
2&
1&
0&
7.6&
7.7&
7.8&
7.9&
8&
8.1&
8.2&
8.3&
8.4&
mode&is&the&8.0P8.9&group&
mode?&
median?&
mean?&
mode?&
median?&
mean?&
8.03&would&give&10&above&
it&and&10&below&it&
3&
10/29/12&
is&central&tendency&enough?&
mode?&
median?&
mean?&
=&160.46&/&20&=&8.02&&
no,&these&data&sets&have&the&same&mean&but&different&variability&
&
we&also&need&to&describe&what&the&variability&is&
measures&of&variability&
measures&of&variability&
range:&the&smallest&score&subtracted&
from&the&largest&score&
&
e.g.,&8.40&–&7.64&=&0.76&
“median&of&8.03&with&range&of&0.76”&
&
&
variance:&average&of&the&squared&difference&
between&the&scores&and&the&mean&
&
standard&devia$on:&the&square&root&of&the&
variance&
standard&devia$on&
e.g.,&or&the&average&distance&of&each&data&point&from&the&mean&
&
standard&devia$on&
probability&distribu8on&graph&
probability&
probability&distribu8on&graph&
68.2%&of&scores&fall&within&
one&standard&devia8on&
from&the&mean&
probability&
1& mean& 1&
stddev&
stddev&
1& mean& 1&
stddev&
stddev&
4&
10/29/12&
standard&devia$on&
standard&devia$on&
probability&distribu8on&graph&
probability&distribu8on&graph&
95.45%&of&scores&fall&
within&two&standard&
devia8ons&from&the&mean&
probability&
99.73%&of&scores&fall&
within&three&standard&
devia8ons&from&the&mean&
probability&
1& mean& 1&
stddev&
stddev&
graphing&mean&and&standard&devia$on&
1& mean& 1&
stddev&
stddev&
graphing&mean&and&standard&devia$on&
Mean&Time&Per&Task&
9&
8&
7&
Time&(s)& 6&
68.2%&of&scores&fall&within&
one&standard&devia8on&
from&the&mean&
5&
4&
3&
2&
1&
0&
Task&1&
Task&2&
Task&3&
Task&4&
differences&between&means&
differences&between&means&
condi$on&one:&
3,&4,&4,&4,&5,&5,&5,&6&
&
&
&
&
&
condi$on&two:&
4,&4,&5,&5,&6,&6,&7,&7&
condi$on&one:&
3,&4,&4,&4,&5,&5,&5,&6&
&
&
&
&
&
condi$on&two:&
4,&4,&5,&5,&6,&6,&7,&7&
Task&5&
Time&for&Task&One&
8&
7&
6&
5&
4&
3&
2&
1&
0&
condi8on&1&
mean&=&4.5&+/&0.9&&
condi8on&2&
mean&=&5.5&+/&1.2&&
is&there&a&sta$s$cally&significant&difference&
between&the&means?&
5&
10/29/12&
tOtest&
different&types&of&distribu$ons&
a&simple&sta$s$cal&test:&allows&one&to&say&
something&about&differences&between&means&at&
a&certain&confidence&level&
&
tPtests&work&on&normal&distribu8ons&
tOtest&
levels&of&significance&
null&hypothesis&of&the&tOtest:&
no&difference&exists&between&the&means&of&two&sets&
of&collected&data&
&
possible&results:&
&
1)&I&am&95%&sure&that&the&null&hypothesis&is&rejected&
e.g.,&there&is&probably&a&true&difference&between&
the&means&
&
2)&I&cannot&reject&the&null&hypothesis&
e.g.,&the&means&are&likely&the&same&
how&certain&do&we&want&to&be?&
&
95%&=&p&<&0.05&(there&is&a&5%&chance&we&are&wrong)&
5&out&of&100&8mes,&this&result&would&occur&by&chance&
&
99%&=&p&<&0.01&(there&is&a&1%&chance&we&are&wrong)&
1&out&of&100&8mes,&this&result&would&occur&by&chance&
&
&
in&HCI,&we&typically&pick&p&<&0.05&or&p&<&0.01&
decide&on&the&p&level&before&tes8ng&
calcula$ng&the&tOtest&
calcula$ng&the&tOtest&
compute&a&tPtest&using&a&
stats&package&
e.g.,&Excel,&SPSS,&JMP&
&
significance:&if&p&<&0.05,&there&is&a&sta8s8cally&
significant&difference&between&the&two&
samples.&&&
&
if&your&nullPhypothesis&said&there&was&no&
difference&(no&effect),&then&reject&it&
1.&select&a&p&value&you&want&to&test&
against,&e.g.,&0.05&
&&
&
2.&compare&each&condi8on’s&column&of&
measurements&in&the&test&
&
3.&tPtest&gives&you&a&pPvalue&
&
&
&
&
6&
10/29/12&
calcula$ng&the&tOtest&
demo&in&Excel&
significance:&if&p&<&0.05,&there&is&a&sta8s8cally&
significant&difference&between&the&two&
samples.&&&
&
if&your&nullPhypothesis&said&there&was&no&
difference&(no&effect),&then&reject&it&
&
no&significance:&if&p&>=&0.05,&there&is&not&a&
sta8s8cally&significant&difference&between&the&
two&samples.&&But&we&cannot&say&they&are&the&
same.&
&
if&your&nullPhypothesis&said&there&was&no&
difference&(no&effect),&then&you&cannot&reject&
it.&&you&also&cannot&accept&it.&
&&
&
different&types&of&tOtests&
different&types&of&tOtests&
unpaired:&comparing&two&sets&of&independent&
observa8ons&
direc$onal&(oneOtailed):&tests&if&data&set&A&is&
greater&than&data&set&B,&but&not&the&other&way&
&
nonOdirec$onal&(two&tailed):&tests&both&
direc8ons&
e.g.,&different&subjects&in&each&group&(between&subjects)&
&
paired:&comparing&two&sets&of&dependent&
observa8ons&
e.g.,&same&subjects&in&each&group&(within&subjects)&
&
most&commonly&we&use&a&twoPtailed&test&because&our&
distribu8ons&are&symmetric&around&the&mean&
types&of&errors&
types&of&errors&
type&1&–&false&posi$ve:&we&see&a&difference&but&
there&isn’t&really&one&
&
type&2&–&false&nega$ve:&we&don’t&see&a&
difference&but&there&really&is&one&
e.g.,&our&samples&happen&to&be&different&because&of&random&sampling.&if&we&
selected&different&samples,&we’d&see&a&difference&
&
&
low&confidence&level&(e.g.,&p&<&0.1):&greater&chance&of&Type&1&errors&
&
&
e.g.,&our&samples&happen&to&be&the&same&because&of&random&sampling.&if&we&
selected&different&samples,&the&samples&would&be&different&
&
high&confidence&level&(e.g.,&p&<&0.0001):&greater&chance&of&Type&2&errors&
&
7&
10/29/12&
single&factor&analysis&of&variance&(ANOVA)&
what&if&we&want&to&compare&more&than&two&sets&
of&data?&
compare&three&or&more&means&
e.g.,&comparing&mousePtyping&on&three&keyboards&
&
qwerty&
&
S1P10&
&
&
&
possible&results:&
alphabe8c&
S11P20&
dvorak&
S21P30&
mouse&typing&is&fastest&on&qwerty&keyboard&
the&same&on&alphabe8c&&&dvorak&
analysis&of&variance&(ANOVA)&
compares&rela8onships&between&many&factors&
&
qwerty&
alphabe8c&
dvorak&
cannot&touch&
type&
S1P10&
S11P20&
S21P30&
can&touch&type&
S31P40&
S41P50&
S51P60&
when&can&we&use&different&descrip$ve&and&
inferen$al&sta$s$cs?&
&
what&type&of&data&do&we&need?&
scales&of&measurements&
scales&of&measurements&
nominal&scale:&numbers&are&used&as&a&name&or&
iden8fier;&no&real&quan8ta8ve&proper8es&
&
ordinal&scale:&numbers&can&be&ordered&or&ranked,&
but&we&don’t&know&the&difference&between&ranks&
&
allowable&stats:&
median&&&percen8les&
&
can&only&count&the&frequencies,&no&allowable&stats&
&
&
&
&
e.g.,&first&place&runner&finished&ahead&of&second&place&finisher&but&we&don’t&know&
by&how&much&they&won&
&
e.g.,&children&rate&their&preference&of&a&new&mouse&compared&to&their&old&one:&
1&–&worst&
2&–&not&as&good&
3&–&neutral&
4&–&bejer&
5&–&best&
&
8&
10/29/12&
scales&of&measurements&
scales&of&measurements&
interval&scale:&numbers&can&be&ordered&and&
we&know&the&difference&between&ranks;&&
zero&is&by&conven8on&
&
allowable&stats:&
mean,&standard&devia8on,&variance,&range,&
tPtest,&ANOVA&
ra$o&scale:&interval&scale&with&an&absolute,&nonP
arbitrary&zero&
&
allowable&stats:&
all&those&for&interval,&coefficient&of&varia8on&
&
&
e.g.,&temperature&in&degrees&C&or&F&
&
e.g.,&Likert&scale&(where&there&is&no&real&“zero”&value)&
1&–&strongly&disagree&
2&–&disagree&
3&–&neutral&
4&–&agree&
5&–&strongly&agree&
e.g.,&temperature&in&degrees&K,&length,&weight,&8me&periods&
e.g.,&how&fast&did&people&perform&on&interface&A&vs.&interface&B&
e.g.,&accuracy&on&interface&A&vs.&interface&B&
&
&
&
&
wrapping&up&
9&